The Martinez Family drove 106.65 miles on the family vacation. They used 7.9 gallons of gasoline. How many miles per gallon of gasoline did they get on the trip?

The measure of each exterior angles of rectangle is 90°

From the question, we have the following parameters that can be used in our computation:

A rectangle

A rectangle is a polygon with 4 sides

So, the measure of the exterior angle can be calculated using the formula for the exterior angles in a polygon

The exterior angles in a polygon are found by using:

Exterior of a rectangle in a polygon =  360°/Number of sides of the polygon

In this case,

The number of sides of the rectangle = 4

So, we have

Exterior of a rectangle =  360°/4

Evaluate

Exterior of a rectangle =  90°

Hence, the value of the measure of each exterior angles of rectangle is 90°

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Complete question

Find the measure of each exterior angles of rectangle?

Step by step​

Answer:

As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.

19+m=38

If you want to solve the equation, just subtract 19 from both sides.

19+m=38

m=19

As a result, the following parametric equations describe the motion of the heat-seeking particle: x = a - 2t and y = b - 4t

As per the question given,

To find the path of a heat-seeking particle placed at point P on a metal plate with a temperature field T(x,y) = 100 - x^(2) - 2y^(2), we need to use the gradient vector of T(x,y).

The gradient of T(x,y) is given by:

∇T(x,y) = (-2x, -4y)

The heat-seeking particle moves in the direction of maximum increase of temperature, so it moves in the direction of the gradient vector, that is, (-2x, -4y).

To find the path of the particle, we need to integrate the gradient vector starting at point P = (a,b), where a and b are the coordinates of the point on the metal plate where the particle is placed.

So the path of the heat-seeking particle is given by the following parametric equations:

x = a - 2t

y = b - 4t

where t is the parameter that represents time.

These equations represent a straight line in the direction of the gradient vector of T(x,y). The particle moves from point P in the direction of the gradient vector, with a speed proportional to the magnitude of the gradient vector.

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\(y = \sqrt[3]{x - 8} \)

When translating the function in the positive x direction, we have to subtract the value from x

The value of angle is ∠P is 140° and ∠Q is 110°.

What do you mean by the exterior and interior angles of a triangle?

The angle between any two of a triangle's three sides is referred to as the interior angle. Any angle that is created when one of a polygon's sides intersects with a line that extends from another side is considered its external angle.

∠P and ∠Q is the exterior angle of the triangle.

we know that the sum of the exterior angle is the sum of the opposite interior angle.

9is the sum of the opposite interior angles that is (110°+30°) = 140°

∠Q is the sum of the opposite interior angles that are (30°+80°)= 110°

Hence,

∠P is 140° and ∠Q is 110°.

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The bearing from the phone to the transmitter is approximately 31 degrees to the east of the north direction.

To determine the bearing from the phone to the transmitter, we can use trigonometry.

The bearing is typically measured clockwise from the north direction.

Given that the transmitter is 13 km west and 21 km south of the phone, we can form a right triangle with the phone as the vertex angle.

The side opposite to the vertex angle represents the north-south direction, and the side adjacent to the vertex angle represents the east-west direction.

Using the tangent function, we can calculate the angle:

tangent(angle) = (opposite side) / (adjacent side)

tangent(angle) = 21 km / 13 km

Taking the inverse tangent (arctan) of both sides, we find:

angle = arctan(21 km / 13 km)

Evaluating this using a calculator, we find the angle to be approximately 58.57 degrees.

However, since the bearing is measured clockwise from the north, we need to subtract this angle from 90 degrees (which represents the north direction) to obtain the bearing:

bearing = 90 degrees - 58.57 degrees

Calculating this, we find the bearing to be approximately 31.43 degrees.

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Answer: 1256.63706

Step-by-step explanation: A=(π20)2

The approximate area of the circle segment bounded by arc DE and chord DE is approximately 17.72 square units.

To approximate the area of the circle segment bounded by arc DE and chord DE, you can use the following formula:

Area = (1/2) * r^2 * (θ - sinθ)

Where:

r is the radius of the circle (r = 20 in your case).

θ is the central angle in radians (47° converted to radians is approximately 0.8203 radians).

Let's calculate it:

θ = 47° * (π / 180) ≈ 0.8203 radians

Now, plug these values into the formula:

Area = (1/2) * (20^2) * (0.8203 - sin(0.8203))

Area ≈ (1/2) * 400 * (0.8203 - 0.7317)

Area ≈ (1/2) * 400 * 0.0886

Area ≈ 17.72 square units

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Arc \(RMP\) has a measure of \(360^{\circ}-120^{\circ}=\boxed{240^{\circ}}\).

Using the tangent-tangent theorem,

\(m\angle RQP=\frac{240^{\circ}-120^{\circ}}{2}=\boxed{60^{\circ}}\)

Answer:

Rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

good luck, i hope this helps :)

Answer: the answer is 7°

Step-by-step explanation:

The constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

A proportional relationship is a mathematical equation that expresses two variables that are in proportion to one another. In this type of relationship, if one variable is multiplied by a certain constant factor, then the other variable will be multiplied by the same constant factor. For example, if the cost of 3 books is $15, then the cost of 6 books will be $30. In this case, the number of books and the cost of the books are in proportion to one another.

The constant of proportionality is the constant factor by which the two variables are multiplied to obtain each other. In other words, it is the ratio between the two variables that remain constant in a proportional relationship. It can be represented by the letter k, and is calculated by dividing one variable by the other.

To find the constant of proportionality from a graph, we need to look at the slope of the line. The slope is the ratio between the change in the y-values and the change in the x-values, which is also known as the rise over run. If the graph shows a proportional relationship, then the slope will remain constant throughout the graph.

For example, if the graph shows the relationship between the number of hours worked and the amount of money earned, and the slope is 10, then the constant of proportionality is 10. This means that for every hour worked, the person earns $10. The equation for this proportional relationship can be written as y = 10x, where y represents the amount of money earned and x represents the number of hours worked.

In conclusion, the constant of proportionality is a crucial aspect of a proportional relationship, as it tells us how much one variable changes in relation to the other. It can be calculated from the equation of the relationship, or from the slope of the graph if it is a linear relationship.

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Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

The given triangle is a right angled triangle. Using trigonometric function we have,

Here, opposite side is VT = 15 and hypotenuse is, TU = 24.

Substituting the values, we have,

Thus, x is approximately 39 degrees.

Answer:

-36 ÷ -3

Step-by-step explanation:

Change in her school lunch account balance per lunch = -3

Total change in her school lunch balance last month = -36

Expression to show number of times Elena bought lunch last month = Total change in her school lunch balance last month ÷ Change in her school lunch account balance per lunch

= -36 ÷ -3

= -36/-3

= 12 times

Elena bought lunch 12 times last month

Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Red line represents the graph of y=x^2

Blue line represents the graph of y=-((x/4)^2)

We can see that the graph was reflected over the x-axis and stretched horizontally.

So, the answer would be the first option.

The mean absolute deviation is $106.6.

Given the table shows the amount Bill spent on 5 days last week.

DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.

Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,

the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:

Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406

The sum of all absolute deviations is:

10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.

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Answer:

4 cups of flour

Step-by-step explanation:

We just need to double 2. The phrase "double" means to multiply by 2 so the answer is 2 * 2 = 4 cups of flour.

The data cited is in the attachment.

Answer: 308.2±106.4

Step-by-step explanation: To construct a confidence interval, first calculate mean (μ) and standard deviation (s) for the sample:

μ = Σvalue/n

μ = 308.2

s = √∑(x - μ)²/n-1

s = 147.9

Calculate standard error of the mean:

\(s_{x} = \frac{s}{\sqrt{n} }\)

\(s_{x}\) = \(\frac{147.9}{\sqrt{12} }\)

\(s_{x}\) = 42.72

Find the degrees of freedom:

d.f. = n - 1

d.f. = 12 - 1

d.f. = 11

Find the significance level:

\(\frac{1-0.97}{2}\) = 0.015

Since sample is smaller than 30, use t-test table and find t-score:

\(t_{11,0.015}\) = 2.4907

E = t-score.\(s_{x}\)

E = 2.4907.42.72

E = 106.4

The interval of confidence is: 308.2±106.4, which means that dental insurance plan varies from $201.8 to $414.6.

The number sentence that gives the best representation of the plants on the upright stand is 8 × 1 = 8.

Given that the plant is said to be upright, then the number of row would be seen as 1.

The rows of the plants are made up of 2 and the plants in them are said to be 4. Hence we would have 4 x 2 = 8

From here we would conclude that 8 × 1 = 8 is the plants on the upright stand.

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The conclusion is option A, we cannot reject the null hypothesis.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

The null hypothesis cannot  be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.

Therefore, we can not reject the hypothesis.

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Answer:72.603

Step-by-step :

70 + 2 + 6 ÷ 10 + 3 ÷ 1000

=72.603

Answer:

8.75

Step-by-step explanation:

7/4 = 1.75 and ?/5 (5x1.75) = 8.75

The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.

Given that,

Use Euler's method with step size 0.5 to compute the approximate y-values y₁, y₂, y₃ and y₄ of the solution of the initial - value problem y' = y-2x. y(2)=1.

We have to find the values y₁

We know that,

At Euler's approach, the curve of the solution can be roughly approximated at steps of h by the tangent in each interval (i.e., by a series of brief line segments). In general, using a short step size improves approximation accuracy.

By Euler approximation,

y₁ = y₀+hf(x₀,y₀)

=1+0.5(1-2(2))

=1-1.5

y₁=-0.5

Similarly,

y₂=-3.25, y₃=-7.825 and y₄=-15.3125

Therefore, The values are y₁=-0.5, y₂=-3.25, y₃=-7.825 and y₄=-15.3125 when the initial - value problem y' = y-2x. y(2)=1.

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Answer:

4 1/2

here! hope this helps!

Answer:

-4

Step-by-step explaition

Answer:

-4

Step-by-step explanation:

edge 2020

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▹ Answer

2,013 cartons

▹ Step-by-Step Explanation

72,468 ÷ 36 = 2,013 cartons

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Answer:

72,468 eggs divided by 36 eggs per carton=2,013 cartons

Step-by-step explanation:

Answer:

Hope I helped!~

Step-by-step explanation:

To find the equation of the line, we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Using the two data points given, we can calculate the slope:

m = (11.25 - 8.35) / (1995 - 1993) = 1.95

To find the y-intercept, we can use one of the data points:

8.35 = 1.95(1993) + b

b = -3884.65

So the equation of the line is:

y = 1.95x - 3884.65

To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:

y = 1.95(6) - 3884.65

y = 11.7 - 3884.65

y = -3872.95

This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.